Energy-based Footstep Localization using Floor Vibration ...
Footstep and Timing Adaptation for Humanoid ... - kobe-u.ac.jp
Transcript of Footstep and Timing Adaptation for Humanoid ... - kobe-u.ac.jp
Footstep and Timing Adaptation for Humanoid Robots Utilizing Pre-computation of Capture Regions
Yuichi Tazaki (Kobe University)
Department of Mechanical Engineering, Graduate School of Engineering, Kobe University
Existing studies on robust walking and balance recovery
✔ Footstep and timing adaptation [Khadiv et al. 2016][Yamamoto et al. 2020]
✔ Center-of-mass height variation [Caron et al. 2018]
Our proposal
✔ Angular momentum variation [Park et al. 2020]
Multi-step v.s. single-step lookahead
- Multi-step lookahead is clearly beneficial for expanding the stabilizable basin
- Real-time implementation without oversimplification is still an open issue
LOW-DIMENSIONAL DYNAMICAL MODEL FOR
CAPTURABILITY ANALYSIS
CAPTURABILITY ANALYSIS METHOD BASED ON
DISCRETIZATION OF STATES
Step duration is lower-bounded by the travel distance of the
swing foot (cannot step too quick)
Horizontal movement is cubic spline Vertical movement is parametrized by the
horizontal movment
Our analysis is based on the following
2D (x, y) centroidal dynamics:
Center-of-mass
Center-of-pressure (aka ZMP)
Instantaneous capture point (aka DCM)
One-step dynamics expressed in the support-foot local coordinate
0-step
N-step (recursive definition)
Variables Swing-foot pose (x, y, and angle)
ICP position (x, y)
• Both expressed in the support-foot local coordinate
ICP inside support region
Swing foot inside allowable range
Not already included in
0 to (N-1)-step basins
Existence of a feasible transition
to the (N-1)-step basin
Efficient 2-phase computation method
For each possible value of ICP, enumerate all combinations
of minimum step duration and landing configuration that
leads to (N-1)-step basin. (enumeration in 7D space)
For each tuple enumerated in Phase 1, enumerate all
possible swing-foot configurations that are reachable to the
landing configuration within the miminum step duration.
Phase 2:
Phase 1:
Definition of N-step viable capture basin
✔ Precomputation of N-step capture basin
✔ Generation of fall-avoiding movement based on multi-step
lookahead with small-enough computation cost for real-time use
Step duration
Capture basin representation based on the discretization of space
ICP grid (x,y)Swing foot configuration
grid (x,y,theta)Capture basin
ICP
grid id
Swing foot
grid id
0-step
1-step
N-step
Naïve implementation requires
enumeration in 11 dimensional space!
ICP
grid id
landing foot
grid id
0.31
0.42
ICP
grid id
landing foot
grid id
Minimum
step duration
(N-1)-step basin
ICP
grid id
ICP domain
The relationship between and determines
a lower-bound on the step duration
ICP
grid id
swing foot
grid id
N-step basin
Position of ICP at landing
(expressed in the current support-foot coordinate)
✔ Fall-avoidance control based on multi-step lookahead while retaining
sufficient level-of-detail of kinematic and dynamic information
SIMULATION RESULTS
Department of Mechanical Engineering, Graduate School of Engineering, Kobe University
Acknowledgement This research was supported by Nagamori Foundation research grant..
SIMULATION MODEL
STEP ADAPTATION THAT UTILIZES PRE-COMPUTED
CAPTURE BASINS
CAPTURE BASIN COMPUTATION RESULTS
Input: Time-to-landing
Planned next state
Current state
Is reachable to without timing adjustment?
Reachable with timing adjustment only?
Adjust timingFind modified target state and timing
Volume of
capture basins
Difference in volume between and is negligible.
0.02[m] x 0.02[m] x 0.05[rad] is considered to have high enough resolution.
ICP
Distribution of
allowable ZMP
Support foot
Swing foot
Distribution of allowable
landing configuration
Visualization of N-step capturable regions
Humanoid robot model used for simualtion
Multi-body model, 31 links, 30 joints
Feasible landing region
Walking without distuabances
Impulsive disturbances during walking
Head: 2 joints (not used)
Body: 2 joints (not used)
Arm: 7 joints (for additional arm swinging)
Leg: 6 joints (for walking)
15Ns
15Ns
Modified footstep
Disturbance injectionStep adaptation
Note: only this step uses precomputed capture basins
ERROR!
No capturable
state found
YES
YES NO
NO
How to adjust timing
Robot model
ICP is on the outer edge of the support foot.
In this case, 1-step capture region is empty.
(>2)-step capture regions are computed.
This ICP is uncapturable by
timing adjustment alone
(i.e., needs step adjustment)
This ICP is capturable by timing
adjustment, provided that the swing-foot
can reach the landing position in time.
Position of ICP at landing
(expressed in the current support-foot coordinate)
How to modify the target state ICP
grid id
Swing foot
grid id
0-step
1-step
N-stepSearch the capture basin database for a next
target state that is reachable from the current
state and minimizes the following cost
function.
Error between modified and desired landing
configuration
Error between modified and desired
ICP at landing
Error between modified and
desired step duration
*AMD Ryzen 9 5950X 3.4GHz, single-core implementation
Run-time computation cost
No adaptation < 1 [us]
Timing adaptation only < 1 [us]
Step & timing adaptation 15 to 30 [ms]
N 0 1 2 3 4 5 6 7 8
Data size [KB] 1,932 33,648 11,166 3,697 1,113 534 369 202 78
Computation
time [ms]
phase 1 19 1,144
3,576
20,321
4,754
8,251
5,261
1,858
4,645
950
4,431
179
3,750
288
3,601
46
2,540phase 2
*AMD Ryzen 9 5950X 3.4GHz, single-core implementation